TY - JOUR
T1 - Oversampled Collocation Approximation Method of Functions via Jacobi Frames
AU - Chen , Xianru
AU - Lin , Li
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 569
EP - 588
PY - 2024
DA - 2024/02
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0071
UR - https://global-sci.org/intro/article_detail/aamm/22929.html
KW - Jacobi polynomial, frame, oversampled, collocation, equispaced sample.
AB - <p style="text-align: justify;">In this paper, we study the Jacobi frame approximation with equispaced
samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in the
uniform norm, especially for differentiable functions. In addition, we show that when
the indexes of Jacobi polynomials $α$ and $β$ are larger (for example max$\{α,β\} &gt; 10$), it
leads to a divergence behavior on the frame approximation error decay.</p>